Unformatted text preview: 3 + e 2t
2 3
3
âˆ’1 âˆ’1 + e 2t
4 3 âˆ’1
âˆ’3
1 [4] Find eAt where A is the matrix
3
3
âˆ’1 âˆ’1 A= Î» = 0, 2 eAt = 1
2 âˆ’1 âˆ’3
1
3 [5] Find eAt where A is the matrix
A= Î» = âˆ’2, 2 eAt = eâˆ’2t
4 1 âˆ’1
âˆ’3 âˆ’1
11
33 [6] Find eAt where A is the matrix
A= âˆ’2 2
âˆ’3 3 , 2 Ã— 2 Exercise Set B (distinct roots), November Î» = 0, 1 eAt = 3 âˆ’2
3 âˆ’2 + et âˆ’2 2
âˆ’3 3 [7] Find eAt where A is the matrix
A= Î» = âˆ’1, 0 2 âˆ’2
3 âˆ’3 eAt = eâˆ’t âˆ’2 2
âˆ’3 3 + 3 âˆ’2
3 âˆ’2 e3t
4 1 âˆ’1
âˆ’3
3 [8] Find eAt where A is the matrix
A= Î» = âˆ’1, 3 eAt = eâˆ’t
4 0 âˆ’1
âˆ’3
2
31
31 + , 2 Ã— 2 Exercise Set C (distinct roots), November 2 Ã— 2 Exercise Set C (distinct roots)
Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where
11
,
22 A= Î» = 0, 3 eAt = 1
3 2 âˆ’1
âˆ’2
1 y(0) = e3t
3 + 11
22 1
0 y= 1
3 2
âˆ’2 + e3t
3 1
2 [2] Solve the di erential equation y = Ay where
A= Î» = âˆ’2, âˆ’1 eAt = eâˆ’2t 0 âˆ’1
,
2 âˆ’3 âˆ’1 1
âˆ’2 2 y(0) = + eâˆ’t 1
2 2 âˆ’1
2 âˆ’1 1
2 y = eâˆ’2t + eâˆ’t 0
0 e2t
4 2
âˆ’2 [3] Solve the di erential equation y = Ay where
A= Î» = âˆ’2, 2 eAt = eâˆ’2t
4 11
33 1 âˆ’1
,
âˆ’3 âˆ’1 + e 2t
4 1
1 y(0) = 3 âˆ’1
âˆ’3
1 y= eâˆ’2t
4 2
6 eâˆ’3t
3 1
âˆ’2 + [4] Solve the di erential equation y = Ay where
A= Î» = âˆ’3, 0 eAt = eâˆ’3t
3 âˆ’1
1
,
2 âˆ’2 1 âˆ’1
âˆ’2
2 + 1
3 1
0 y(0) = 21
21 y= + 1
3 2
2 [5] Solve the di erential equation y = Ay where
A= Î» = âˆ’1, 2 eAt = eâˆ’t
3 11
,
20 1 âˆ’1
âˆ’2
2 + e 2t
3 y ( 0) = 21
21 1
2 y= eâˆ...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.
 Spring '14
 DaveBayer
 Linear Algebra, Algebra

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